1. Heliosphere: Solar Wind
CSI 662 / ASTR Lect. 05, February Spring 2007
Heliosphere: Solar Wind
References:
Gombosi: Chap. 12, P236 – P252 (main reference)
Tascione: Chap. 3, P31-P40 (supplement)
Prolss: 6.1– 6.2, P277-P314 (supplement)
Update on 2007/03/15

2. Ideal MHD: Frozen-in effect
Reference
Prolss A.14, P484-P487
The magnetic flux passing through a closed curve that moves with the plasma flow velocity remains constant
Plasma elements connected at any point in time by a common magnetic field line remain connected by a common field line

3. What is Solar Wind?
Solar wind is the continuous flow of plasma outward from the Sun through the solar system
It was recognized in 1950s by observing the tails of comets: the straight blue tail could be driven by plasma flow

4. What Causes Solar Wind?
High thermal pressure in hot corona overcomes the gravitational constraints, resulting in coronal expansion
Extremely low pressure (10 orders of magnitude smaller) in interstellar medium can not contain the coronal pressure
Expansion becomes supersonic

5. Solar Wind Solution More on solar wind
If you neglect the effect of heat conduction and magnetic fields:
Aassuming isothermal corona: so p=npkT+nekT = 2kT/mpρ
Ref: Gombosi 12.1, P236
More on solar wind

6. Problems with Static corona
Solar Wind Solution (cont.)
If we assume stationary solar atmosphere (u=0)
Where the index B indicate the Base of the corona
As r
For TB ~ 106 K
p ~ 3 x10-4 pB >> any reasonable interstellar
Pressure!!! So a Hot Static Corona cannot exist
Problems with Static corona

7. Solar Wind Solution (cont.)
Parker Solution: (neglecting electromagnetic effects) (1958)
The momentum equation:
is the local sound speed.

8. Solar Wind Solution (cont.)
Critical distance where kinetic energy equals gravitational energy
Type V solution gives the right solar wind: sonic speed at the critical distance

9. Solar Wind Solution (cont.)
Parker’s solution for different coronal temperatures
For example, for T=106K, and coronal density of 2x108cm-3, rc=6Rs. The solar wind accelerates to up to 40RS, and afterwards propagates to a nearly constant speed of 500km/s
lachzor page 239 T. Gombosi

10. Solar Wind Structure Archimedean Spiral Garden Sprinkler Analogy
Jetlines that connect the flow elements from the same differentially small source region form an Archimedean spiral
However, the streamline, along which an individual flow element is flowing, is strictly radial

11. Solar Wind Structure Φ :the azimuth angle of magnetic field line at r
Φ0: the azimuth angle of magnetic field footpoint at the source surface
Rs: source surface, e.g., 3 Rsun
Usw: solar wind speed, e.g., 400 km/s
Ω: solar rotation, 2.7 X 10-6 radians/sec
At the Earth, r = 1 AU, Φ0 = ~ 45°
When the plasma flow arrives at the Earth, the solar source has rotated 45°

12. Interplanetary magnetic Field (IMF) structure
Frozen-in theorem: Plasma elements connected at any point in time by a common magnetic field line remain connected by a common field line
Since the plasma flow in a single spiral jet-line originates from a common source, the IMF should follow the jet-line, thus also display an Archimedean spiral pattern.
Magnetic field is rooted in the photospheric surface of the Sun
At certain height in the corona (e.g., 3 Rs), all magnetic field lines open and point radially. A surface of this is called source surface
The spiral pattern can be traced back to the source surface

13. IMF
Frozen-in Theorem: The magnetic flux passing through a closed curve that moves with the plasma flow velocity remains constant
Because magnetic field along the jetline

14. IMF Bs: magnetic field at the source surface Θ: polar angle
(fall more slowly!)
As we go outward in the solar system
the magnetic field becomes more and more
azimuthal

15. IMF

16. The End